GCSE (9–1) Mathematics - ocr.org.uk

1 GCSE (9 1) MathematicsHJ560/04 Paper 4 (Higher Tier)Practice PaperDate Morning/AfternoonTime allowed: 1 hour 30 minutesYou may use: A scientific or graphical calculator Geometrical instruments Tracing paper**000000000000**0000000000*First nameLast nameCentreCandidatenumbernumberINSTRUCTI ONS Use black ink. You may use an HB pencil for graphs and diagrams. Complete the boxes above with your name, centre number and candidate number. Answerallthe questions. Read each question carefully before you start your answer. Where appropriate, your answers should be supported with working.

2 Marks may begiven for a correct method even if the answer is incorrect. Write your answer to each question in the space provided. Additional paper may be used if required but you must clearly show your candidatenumber, centre number and question number(s). Donotwrite in the bar The total mark for this paper is100. The marks for each question are shown in brackets[ ]. Use the button on your calculator or take to be unless the question saysotherwise. This document consists of20pages. OCR 2015J560/04 Turn over[601/4606/0]2 Answerallthe questions1 (a)The attendance at a football match was 67500, correct to the nearest hundred.

3 (i)What was thehighestpossible attendance?(a)(i)..[1](ii)What was thelowestpossible attendance?(ii)..[1](b)A distance,d, was given as m,truncatedto 2 decimal the error interval for the distance, d<..[2] OCR 2015J560/0432 The population,P, of an islandtyears after January 1st 2016 is given by this (a)What was the population of the island on January 1st 2016?(a)..[1](b)Explain how you know that the population is [1](c)What is the annual percentage increase in the population?(c).. %[1](d)Work out the population of the island on January 1st 2021.

4 (d)..[2] OCR 2015J560/04 Turn over43A shop has a sale that offers 20% off all the final day they reduce all sale prices by 25%.Alex buys a hairdryer on the final out theoverallpercentage reduction on the price of the %[6] OCR 2015J560/0454An interior angle of a regular polygon is eleven times its exterior out the number of sides of the [4] OCR 2015J560/04 Turn over65 (a)Find thenth term of this linear (a)..[2](b)Here is a quadratic expression for thenth term of this sequence ispn2+ the value ofpand the value ofq.(b)p=..q=..[4] OCR 2015J560/0476 Some of the children at a nursery arrive by car.

5 40% of the children at the nursery are boys. 70% of the boys at the nursery arrive by car. 60% of the girls at the nursery arrive by is the probability that a child chosen at random from thenursery arrives by car?..[5] OCR 2015J560/04 Turn over87 The rectangle ABCD represents a to scaleThe lines show all the paths in the circular path is in the centre of the rectangle and has a diameter of 10 the shortest distance from A to C across the park, using only the paths m[6] OCR 2015J560/0498 Eddie and Caroline are going to the school buys 6 adult tickets and 2 child tickets.

6 He pays buys 5 adult tickets and 3 child tickets. She pays out the cost of an adult ticket and the cost of a child ticket ..Child ticket ..[5] OCR 2015J560/04 Turn over109 Gavin measures the heights of 80 plants he has table summarises his ,hcm0<h 5050<h 100100<h 125125<h 150 Number of plants838313(a) (i)Complete the cumulative frequency table ,hcmh 50h 100h 125h 150 Cumulative frequency8[2](ii)Draw the cumulative frequency 25 5075100 125 150 CumulativefrequencyHeight (cm)[2] OCR 2015J560/0411(b)Ted asks if Gavin has 10 plants over 120cm in why Gavin cannot be certain that he has 10 plants overthis [1](c)

7 Gavin sells these 80 plants using the price list ,hcmh 8080<h 120h>120 Price ( ) plant costs him 60p to the total profit Gavin will receive when he sells allthese plants.(c) ..[6] OCR 2015J560/04 Turn over1210 The diagram shows a circle, centre P, Q, R and S lie on the circumference of the is a tangent to the RPS=44 and angle PSO=32 .UTSOPRQ32 44 x y Not to scale(a)Work out the value ofx.(a)x=..[4](b)Work out the value ofy.(b)y=..[3] OCR 2015J560/041311In the diagram, ABC is a triangle and line BD is perpendicularto BAC=43 , BD=8 cm and AC= cm43 Not to scaleCalculate angle [6] OCR 2015J560/04 Turn over1412 Show thatk=4+3j5 jcan be rearranged toj=5k 43+k.

8 [4] OCR 2015J560/041513 (a)yis directly proportional to 75 whenx= a formula linkingxandy.(a)..[3](b)yis inversely proportional tox2andy=3 whenx= thaty=27 whenx=4.[3] OCR 2015J560/04 Turn over1614 (a)Writex2+10x+29 in the form x+a 2+b.(a)..[3](b)Write down the coordinates of the turning point of the graph ofy=x2+10x+29.(b)( .. , .. )[1] OCR 2015J560/041715 (a)Complete the table fory=x3 6x [2](b) (i)Between which twoconsecutive integersis there a solution to the equationx3 6x 5=0?Give a reason for your solution lies betweenx=.. andx=.

9 Because ..[2](ii)Choose a value ofxbetween the two values you gave in part(b)(i).Calculate the corresponding value ofy.(b)(ii)x=..y=..[2](iii)State a smaller interval in which the solution lies.(iii)..[1] OCR 2015J560/04 Turn over1816 Solve these simultaneous equations 3y=2x2+8x 7x=.. ,y=..x=.. ,y=..[6] OCR 2015J560/041917 (a)Show that 396 can be written as 6 11.[2](b) Withoutusing a calculator, show that4+2 22 2can be simplified to 6+4 2.[6] OCR 2015J560/0420 PLEASE DO NOT WRITE ON THIS PAGEC opyright InformationOCR is committed to seeking permission to reproduce all third-party content that it uses in the assessment materials.

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